Shared Classical Randomness Proves Scalable Advantage for Quantum Generative Models

A new paper on arXiv (2608.05110) demonstrates that shared classical randomness can establish a strict representational separation between channel quantum generative models and unitary Born models at fixed shallow depth, for arbitrarily large systems. The research addresses a key limitation of near-term quantum hardware, which restricts circuit depth and connectivity, thereby limiting the output distributions of shallow unitary Born models. By augmenting bounded-connectivity shallow unitary circuits with shared classical randomness, the authors prove a scalable advantage, showing that channel models can represent a strictly larger family of distributions than their unitary counterparts. This result extends previous small-scale findings to arbitrarily large systems, resolving an open question in the field. The work has implications for quantum generative modeling, suggesting that incorporating stochasticity via shared randomness can enhance the expressive power of quantum models without requiring deeper circuits or more complex entanglement. The paper is categorized as a cross announcement and was submitted on August 26, 2025 (arXiv:2608.05110v1).